Paul Evans gave the hosts a deserved first-half lead with a simple tap-in on 25 minutes.
But Ipswich hit back shortly after the interval, Darren Bent reacting sharply to turn Jason de Vos' header into the bottom corner.
Andy Reid created chances for Gareth Taylor and Paul Evans to score the winner but it was not to be for Forest.
Nottingham Forest boss Joe Kinnear on Spurs target Andy Reid:
"I would like to keep him permanently, but unfortunately it is not up to me.
"The chairman has struck a deal, and if someone comes up with £5m he goes.
"We have scouts from Manchester United, Liverpool and Arsenal coming here - and they are also looking at him.
"For £5m someone is going to get a hell of a player, and if I were a Premiership manager the first thing I would do is sign him up on a five-year contract."
Ipswich boss Joe Royle:
"I am delighted with a point because in the second half we didn't play.
"Kelvin Davis was excellent in goal, and Tony Dinning had a good debut. But after that I am looking for people to step up.
"Having said that, not many teams will come to Forest and win. I suppose their season hinges on whether they can keep Andy Reid; he is an excellent player."
Nottm Forest: Gerrard, Louis-Jean, Doig, Hjelde, Rogers, Impey, Evans, Jess (James 90), Reid, Johnson, Taylor.
Subs Not Used: King, Roche, Perch, Gardner.
Goals: Evans 25.
Ipswich: Davis, Diallo, De Vos, Naylor, Richards, Miller, Horlock, Westlake, Dinning, Bent, Kuqi (Bowditch 84).
Subs Not Used: Wilnis, Counago, Price, Mitchell.
Booked: De Vos.
Goals: Bent 54.
Ref: A Kaye (W Yorkshire).